Dear friends, <<A cable of constant mass per unit length (p) points straight up hovering over a point on the Equator. How long has to be the cable?>> I believe there's a mistake in my answer and I need somebody to give me a hint. What I've done is: integrate dF(gravitational force) over the whole string of length L. So the net force equals the centrifugal acceleration times mass, in the centre of mass. Doesn't it? so i get mw^2(R+L/2)=GMm/(R(R+L)) where R is the Earth radius and w it's angular velocity. A friend of mine has told me that I'm missing the stress (tension) in this answer. Thanks for your help.